Syllabus scavenger hunt for Math 215
Answer the following based on the course syllabus. Raise hands when completed.
- What is the most important "required" thing to bring to class?
- Is book homework graded?
- Is WeBWorK graded?
- Which recommendation will be most useful?
- If you have a non-authorized absence but complete the assignment before the instructor returns it to the class, how much credit is it worth?
- What are "MP"? How many MP do you start with?
- When is WeBWorK due?
- What is special about the quizzes?
- How can you find the instructor's Drop-in times?
- Ask one question about the course.
Limits review
Compute the following limits.
- \( \displaystyle\lim_{n \to \infty} \dfrac{\ln(n)}{3n} \) \(= 0 \)
- \( \displaystyle\lim_{n \to \infty} \dfrac{8 + 3^n}{4 + 8^n} \) \(= 0 \)
- \( \displaystyle\lim_{n \to \infty} \dfrac{\sqrt{n}}{n + 3} \) \(= 0 \)
- \( \displaystyle\lim_{n \to \infty} \dfrac{n^4 + 2n}{n^3 - 1} \) \(= \infty \)
Derivative review
Compute the following derivatives.
- \( \dfrac{d}{dx} \left( x^2 + \sqrt{x} + x^{-1} - \dfrac{1}{x^2} \right) \) \(= 2x + \dfrac{1}{2 \sqrt{x}} - x^{-2} + \dfrac{2}{x^3} \)
- \( f(x) = \sin(x) \) , \(f'(x) = \cos(x) \)
- \( f(x) = \cos(x) \) , \(f'(x) = -\sin(x) \)
- \( f(x) = \tan(x) \) , \(f'(x) = (\sec(x))^2 \)
- \( \dfrac{d}{dt} \left( t^{1/2} \sin(t) \right) \) \(= t^{1/2} \cos(t) + \frac{1}{2} \sin(t) t^{-1/2} \)
- \( f(x) = \dfrac{\ln(x)}{x} \) , \(f'(x) = \dfrac{1-\ln(x)}{x^2} \)
- \( \dfrac{d}{dy}( \ln(\tan(y))) \) \(= (\sec(y))^2 \dfrac{1}{tan(y)} = \csc(y) \sec(y) \)
Integration review
Compute the following integrals.
- \( \displaystyle\int_{}^{} \left(x^2 + \frac{1}{x^2} + \frac{1}{x} \right) \,dx \) \(= \frac{1}{3} x^3 - \frac{1}{x} + \ln|x| + C \)
- \( \displaystyle\int_{}^{} 5 e^x \,dx \) \(= 5 e^x + C \)
- \( \displaystyle\int_{}^{} \sin(x) \,dx \) \(= -\cos(x) + C \)
- \( \displaystyle\int_{}^{} \cos(x) \,dx \) \(= \sin(x) + C \)
- \( \displaystyle\int_{}^{} e^{2x}\,dx \) \(= \frac{1}{2} e^{2x} + C \)
- \( \displaystyle\int_{1}^{5} (2x + 1) \,dx \) \(= 28 \)